The words Harvard and knee-jerk are not often seen in the same sentence, but when a rumoured shortlist of candidates to succeed outgoing president Larry Summers pops up and the majority of the names on it are women, there is good cause.

Summers resigned in February after less than five years at the helm of America's flagship university, essentially because his irresistible force met an immovable object called the faculty of arts and sciences. He ebulliently tried to take charge, the two combusted and Larry got fried.

But what the world remembers most about Summers is that he claimed there were so few women at the very top of science and maths because they innately have a lesser aptitude for those fields than men. Cue uproar.

Since he fell on his sword to escape yet another censure vote by his opponents, the most exciting names bandied around in the US press as most likely to succeed him are all women. The three big guns are insiders: Elena Kagan, dean of Harvard law school, Drew Faust, head of the university's Radcliffe Institute of advanced study, and Harvard old girl Amy Gutmann, president of the University of Pennsylvania. A few good men

The former president of Duke University Nan Keohane has been mentioned, but quickly and loudly appeared to rule herself out, while rising star Ruth Simmons of Brown, the first African-American Ivy League president, is a thrilling wild card. As an afterthought, a few men have also been mentioned.

"This could be the decade of the woman president," says Nancy Hopkins, biology professor at Massachusetts Institute of Technology and an expert on women's role in the arts and sciences. Does she mean at Harvard, the White House in 2008, or both? "I think the White House is going to take a little longer," she says. "But they made a woman president of Princeton; after that, anything was possible."

Princeton's president since 2001, Shirley Tilghman, has been enthusiastically put forward for the Harvard shortlist by a fellow Princeton professor, Cornel West - who defected there from Harvard following an early, ugly clash when Summers accused him of neglecting scholarly rigours after he recorded a hip-hop CD.

Proponents of a female president are aware they risk controversy. "You want the best person," says Hopkins. "But if it was a 50-50 choice, I cannot tell a lie that I would want them to appoint a woman."

Summers' spat with West over the CD and his comments about women were as damaging as his vigorous pro-Israeli stance was controversial, but they did not cause his downfall. The crisis stemmed from his mission to exert his authority and exact rapid and radical modernisation, pressuring star professors to, as he saw it, swan less and teach more, produce more competitive applied research, pool faculty resources and expand the sciences.

This is what he was appointed for, but coming from a more centralised government set-up, where he was Bill Clinton's treasury secretary, to the highly decentralised Harvard, he shook up faculties and fiefdoms with an abrasive and autocratic style that spawned enemies.

When Summers ultimately engaged in a death-wrestle with the dean of the core faculty of arts and sciences, William Kirby, it sparked one no-confidence vote at the university and was leading imminently to a second when he resigned.

"Everyone was convinced that Summers was what Harvard needed," says one research associate, who asked not to be identified. "But he was a really tough guy for most people to take, and reform was not necessarily what people wanted or could tolerate in a culture of resistance."

"We need a good leader who is acquainted with the very broad range of disciplines taught in the liberal arts college at Harvard," says Judith Ryan, Harvard professor of German and comparative literature. "Summers tended to translate every issue into economics, his speciality."

Many believe his successor should not abandon Summers' vision, but should execute something similarly ambitious more diplomatically. "We need someone with a proven record in academic leadership," says Hopkins.

As much as she personally would like to see a woman at the helm, she also speaks highly of one of the three men so far tipped to be in the running, Lawrence Bacow, a former chancellor of MIT and now president of Tufts University. The other men mentioned are Harvard provost Steven Hyman and Stanford provost John Ethemendy.

Gutmann, a philosopher and political scientist, was a finalist in the last presidential search and is a Harvard alumnus, which will work in her favour. Faust, a renowned historian, has been a leading force at Harvard since she arrived in 2001 and led the diversity committee set up by Summers to improve women's prospects - after he had apologised for his remarks. She could be seen as tainted by association with Summers, however. The insider

Cornel West has called for someone with "decency, empathy, maturity and vision", praising Simmons and Gutmann, as well as Tilghman. But the front-runner so far is Kagan, and many believe the university will go for an insider this time.

At just 45, she has headed the law school for only three years, but has won acclaim for bringing vigorous modernisation without making significant enemies. She is already being talked of as a potential future Supreme Court justice.

She broke a logjam over the appointment of professors, made herself popular with students by improving facilities and developed a reputation for arbitrating the kind of debates that can sink projects with politics. Fans hope she could engineer a renaissance for the whole university.

They will be in for a long wait, however. The new president will be picked by the seven-member executive board that runs the university, known as the Harvard Corporation. But Summers is in post until the summer and will be replaced on an interim basis by past president Derek Bok, perhaps for as long as a year, while the search for a successor goes on.

"Why anyone would want the Harvard job at the moment, I don't know, given the mess that they will inherit," says Daniel Fisher, physics professor at Harvard, who was a Summers adversary. "We are hoping Bok can repair some of the damage that has been done and reverse some of Summers' decisions. If he can do enough of that, then the new president can start with a clean slate."

There is no such thing as a clean slate at a 350-year-old university, although appointing its first woman president could be counted as coming close.